Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box so that the product is as close to 50 as possible.
Hint
What whole numbers would you multiply to make it as close to 50 as possible?
Closest is defined as the absolute value of the difference between the product and 50.
Closest is defined as the absolute value of the difference between the product and 50.
Answer
The closest products found are 50.02 (6.1 x 8.2) from a student in Shannon Andrews‘ class as well as 49.98 (9.8 x 5.1) from a student in Lauren Giordano’s class.
Source: Robert Kaplinsky
A student found 9.8 x 5.1 = 49.98
Awesome! I updated the answer accordingly. Thanks for the heads up.
8.2*6.1
A quick Desmos graph to show some possible products.
https://www.desmos.com/calculator/ebumroskuv
That’s really cool, Rusty! Thanks for sharing that.
Hi Rusty, I modified your graph a little. Thanks for giving me the idea.
https://www.desmos.com/calculator/xlbdjd8l8b
What about 7*7=49?
Can only use each number once!
Is the problem as close to 50 without going over because I don’t see anything about that? If not, 8.2 x 6.1 is 50.02 and two hundredths away from 50 which is equal to 9.8 x 5.1 = 49.98 (distance wise).
Never mind, I just saw it was added to the answers and I must have missed that!
9.8 x 5.1=49.98 or 6.1 x 8.2=50.02
50.02
Now – I have tried some open middle problems, and I can usually see an ‘algorithm’ to get to an answer. For this one, all I could see was divide 50 by a number, say 8.7, and if the answer has minimal rounding, you get a closer answer to 50. But to find 8.2 x 6.1, it took me 8 tries and I did not consider the 9.8 x 5.1!
Was this pretty much a guess and check?
Honestly, your strategy sounds pretty far from “guess and check”. Guess and check would be picking random numbers out of a hat and using those each time. You used your conceptual understanding to strategically choose great numbers and narrow in on the best options. Well done.
“The closest products found are 50.02 (6.1 x 8.2) from a student in Shannon Andrews‘ class as well as 49.98 (9.8 x 5.1) from a student in Lauren Giordano’s class. ”
I checked. These are the closest products to 50 possible. There are no better solutions.
5.1 x 9.8 = 49.98